Petrochemical products such as oil and gas are ubiquitous in society and can be found in everything from gasoline to children's toys. Because of this, the demand for oil and gas remains high. In order to meet this high demand, it is important to locate oil and gas reserves in the Earth. Scientists and engineers conduct “surveys” utilizing, among other things, seismic and other wave exploration techniques to find oil and gas reservoirs within the Earth. These seismic exploration techniques often include controlling the emission of seismic energy into the Earth with a seismic source of energy (e.g., dynamite, air guns, vibrators, etc.), and monitoring the Earth's response to the seismic source with one or more receivers in order to create an image of the subsurface of the Earth. By observing the reflected seismic wave detected by the receiver(s) during the survey, the geophysical data pertaining to reflected signals may be acquired and these signals may be used to form an image of the Earth near the survey location.
In marine-based acquisitions, the receiver(s) may measure the seismic wave after it is reflected from the sub-surface of the earth. The reflection from the sub-surface may, however continue upwards to the surface of the water, where it may again be reflected by the boundary between the water and the air above the water. Because the water-air boundary is a near perfect reflector, the seismic wave is reflected from the water-air boundary and propagates back towards the sub-surface. The downwardly reflecting seismic wave is detected by the receivers and is commonly known as a receiver-side “ghost.” In some cases, the ghost may again reflect off of the sub-surface, and again reflect off of the water-air boundary, thus creating multiple reflections. Also, a source-side ghost may be present, which is similar to the receiver-side ghost except the source-side ghost is the seismic signal that propagated upwards to the water-air boundary from the source which then reflects off of the sub-surface.
The ghost limits the amount of energy in the seismic wavelet at very low frequencies and at higher frequencies determined by the streamer depth. Also, the phase of the seismic data is distorted around the ghost notch frequency. Surveys have historically been designed with sources and receivers towed at a relatively shallow depth in order to effectively capture the higher frequencies desired for the targets. Towing sources and streamers at a relatively shallow depth, however, can lead to distortion of low frequencies because of the increased susceptibility to noise generated by waves at the sea surface. More recently, methods have been developed to reduce ghosts and allow receivers to be towed at deeper depths by a number of methods, including specific processing methods, towing the receivers at varying depths, towing combinations of streamers at differing depths, and towing receivers with both pressure and particle motion sensors. As deghosting techniques improve and higher frequencies are recovered from the data, the limitations of streamer separation may become a limiting factor on the bandwidth of the image because it can be difficult to economically achieve adequate spatial sampling in the cross line direction.
One potential solution to the inadequate spatial sampling problem is to use some form of interpolation to predict measurements at locations in between streamers that were not physically sampled by the receivers on the streamers. Interpolation may include fitting measured seismic data to a model (e.g., using a least squares or complex conjugate method), and then extending that model to project what the seismic wavefield would have looked like had it been measured at locations in between the streamers in the same plane as the streamers. Because interpolation, by definition, involves fitting data to a model, it can introduce inaccuracies, which can subsequently propagate (and be amplified) through the remainder of the seismic data processing sequence.